dorsal/arxiv
View SchemaRemodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network
| Authors | E. Kuhl, K. Garikipati, E. M. Arruda, K. Grosh |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0411037 |
| URL | https://arxiv.org/abs/q-bio/0411037 |
| DOI | 10.1016/j.jmps.2005.03.002 |
Abstract
A new class of micromechanically motivated chain network models for soft biological tissues is presented. On the microlevel, it is based on the statistics of long chain molecules. A wormlike chain model is applied to capture the behavior of the collagen microfibrils. On the macrolevel, the network of collagen chains is represented by a transversely isotropic eight chain unit cell introducing one characteristic material axis. Biomechanically induced remodeling is captured by allowing for a continuous reorientation of the predominant unit cell axis driven by a biomechanical stimulus. To this end, we adopt the gradual alignment of the unit cell axis with the direction of maximum principal strain. The evolution of the unit cell axis' orientation is governed by a first-order rate equation. For the temporal discretization of the remodeling rate equation, we suggest an exponential update scheme of Euler-Rodrigues type. For the spatial discretization, a finite element strategy is applied which introduces the current individual cell orientation as an internal variable on the integration point level. Selected model problems are analyzed to illustrate the basic features of the new model. Finally, the presented approach is applied to the biomechanically relevant boundary value problem of an in vitro engineered functional tendon construct.
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"abstract": "A new class of micromechanically motivated chain network models for soft\nbiological tissues is presented. On the microlevel, it is based on the\nstatistics of long chain molecules. A wormlike chain model is applied to\ncapture the behavior of the collagen microfibrils. On the macrolevel, the\nnetwork of collagen chains is represented by a transversely isotropic eight\nchain unit cell introducing one characteristic material axis. Biomechanically\ninduced remodeling is captured by allowing for a continuous reorientation of\nthe predominant unit cell axis driven by a biomechanical stimulus. To this end,\nwe adopt the gradual alignment of the unit cell axis with the direction of\nmaximum principal strain. The evolution of the unit cell axis\u0027 orientation is\ngoverned by a first-order rate equation. For the temporal discretization of the\nremodeling rate equation, we suggest an exponential update scheme of\nEuler-Rodrigues type. For the spatial discretization, a finite element strategy\nis applied which introduces the current individual cell orientation as an\ninternal variable on the integration point level. Selected model problems are\nanalyzed to illustrate the basic features of the new model. Finally, the\npresented approach is applied to the biomechanically relevant boundary value\nproblem of an in vitro engineered functional tendon construct.",
"arxiv_id": "q-bio/0411037",
"authors": [
"E. Kuhl",
"K. Garikipati",
"E. M. Arruda",
"K. Grosh"
],
"categories": [
"q-bio.QM",
"q-bio.TO"
],
"doi": "10.1016/j.jmps.2005.03.002",
"title": "Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network",
"url": "https://arxiv.org/abs/q-bio/0411037"
},
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